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CHROMATOGRAPHY

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CHROMATOGRAPHY

Principles and Instrumentation

Mark F. Vitha

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Copyright © 2017 by John Wiley & Sons, Inc. All rights reserved

Published by John Wiley & Sons, Inc., Hoboken, New JerseyPublished simultaneously in Canada

No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by anymeans, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted underSection 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of thePublisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center,Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web atwww.copyright.com. Requests to the Publisher for permission should be addressed to the PermissionsDepartment, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, oronline at http://www.wiley.com/go/permissions.

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Library of Congress Cataloging-in-Publication Data:

Names: Vitha, Mark F.Title: Chromatography : principles and instrumentation / Mark F. Vitha.Description: Hoboken, New Jersey : John Wiley & Sons, Inc., [2017] | Includes

bibliographical references and index.Identifiers: LCCN 2016011576| ISBN 9781119270881 (cloth : alk. paper) | ISBN

9781119270898 (pdf : alk. paper) | ISBN 9781119270904 (epub : alk. paper)Subjects: LCSH: Chromatographic analysis. | Gas chromatography. | Liquid

chromatography.Classification: LCC QD79.C4 V58 2017 | DDC 543/.8–dc23 LC record available at

http://lccn.loc.gov/2016011576

About the cover: A two-dimensional liquid chromatography (LC × LC) separation of maize seed extract.Ground seed was extracted using methanol mixed with a phosphate buffer (pH 5.7) followed by solid phaseextraction prior to analysis. The first dimension separation used a Zorbax SB-C3 column while a carbon-cladcore-shell silica column was used for the second dimension. Additional experimental details about theextraction and chromatographic system can be found in Huang, Y.; Gu, H.; Filgueira, M.; Carr, P.W.J. Chromatogr. A, 1218, 2011, 2984–2995 and Filgueira, M.; Huang, Y.; Witt K.; Castells C.; Carr, P.W. Anal Chem.83, 2011, 9531–9539. The author thanks the creators of this image for their permission to use this image andMarcelo Filgueira for the work he put into it for this book.

Typeset in 10/13pt PalatinoLTStd-Roman by SPi Global, Chennai, India

Printed in the United States of America

10 9 8 7 6 5 4 3 2 1

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CONTENTS

PREFACE ix

1. Fundamentals of Chromatography 11.1 Theory 1

1.1.1 Component Separation 31.1.2 Retention Factor 61.1.3 Separation 111.1.4 Resolution and Theoretical Plates 13

1.2 Band Broadening 201.2.1 Diffusion 211.2.2 Linear Velocity 231.2.3 Broadening in Open Tubes with No Stationary Phase

and No Retention 241.2.4 Broadening in Open Tubes with a Stationary Phase 281.2.5 Broadening in a Packed Column 341.2.6 Putting It All Together 431.2.7 Practical Consequences of Broadening Theory 45

1.3 General Resolution Equation 471.4 Peak Symmetry 511.5 Key Operating Variables 511.6 Instrumentation 531.7 Practice of The Technique 53

1.7.1 Quantitation 531.7.2 Internal Standards and the Method of Standard Additions 55

1.8 Emerging Trends and Applications 551.9 Summary 55

Problems 56References 59Further Reading 59

2. Gas Chromatography 612.1 Theory of Gas Chromatographic Separations 61

2.1.1 GC Columns and Partitioning 642.2 Key Operating Variables that Control Retention 64

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vi CONTENTS

2.2.1 Adjusting Retention Time: Temperature 652.2.2 Adjusting Retention Time: Temperature Programming 672.2.3 Adjusting Retention Time: Mobile Phase Flow Rate 692.2.4 Adjusting Retention Time: The Column and the Stationary

Phase 722.2.5 Adjusting Retention Time: Summary 782.2.6 Measures of Retention 78

2.3 Gas Chromatography Instrumentation 822.3.1 Carrier Gas Supply 832.3.2 The Injection Port and the Solute Injection Process 832.3.3 Oven/Column Compartment 972.3.4 Detectors 98

2.4 A More Detailed Look at Stationary Phase Chemistry: Kovats Indicesand Mcreynolds Constants 1112.4.1 Kovats Retention Indices 1112.4.2 Stationary Phase Selection 120

2.5 Gas Chromatography in Practice 1242.5.1 Syringe Washing 1242.5.2 Controls and Blanks/Ghost Peaks 1242.5.3 Autosamplers 1252.5.4 GC Septa 1252.5.5 Qualitative Analysis 1262.5.6 Quantitative Analysis 1262.5.7 Derivatization 1282.5.8 High-Speed GC 1282.5.9 Tandem GC 1292.5.10 Microfabricated GC 129

2.6 A “Real-World” Application of Gas Chromatography 1312.6.1 GC and International Oil Trading 131

2.7 Summary 136Problems 137References 143Further Reading 144

3. Liquid Chromatography 1453.1 Examples of Liquid Chromatography Analyses 1453.2 Scope of Liquid Chromatography 1473.3 History of LC 148

3.3.1 Modern Packing Materials 1493.4 Modes of Liquid Chromatography 152

3.4.1 Normal Phase Liquid Chromatography (NPLC) 1523.4.2 Reversed-Phase Liquid Chromatography (RPLC) 1543.4.3 Ion-Exchange Chromatography (IEX) 1653.4.4 Hydrophilic Interaction Chromatography (HILIC) 173

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CONTENTS vii

3.4.5 Size Exclusion Chromatography (SEC) 1753.4.6 Affinity Chromatography 178

3.5 HPLC Instrumentation 1803.5.1 The Proportioning Valve 1813.5.2 Mixing Chamber 1813.5.3 Pumps 1813.5.4 Injection 1833.5.5 The Column and Particles 1853.5.6 Guard Columns 1873.5.7 Detectors 188

3.6 Specific Uses of and Advances in Liquid Chromatography 2013.6.1 Chiral Separations 2023.6.2 Preparative-Scale Chromatography 2073.6.3 Ultra-High Performance Liquid Chromatography (UHPLC)

for High-Speed Separations 2123.6.4 Tandem-Column Liquid Chromatography 2163.6.5 Two-Dimensional Liquid Chromatography (2D-LC) 218

3.7 Application of LC – Analysis of Pharmaceutical Compounds inGroundwater 2243.7.1 Sampling 2253.7.2 Analysis Method for 21 Antibiotics – Sample Pretreatment 2253.7.3 Use of Internal Standards and Other Quality Assurance

Issues 2273.7.4 LC Analyses 2283.7.5 Mass Spectrometric Selected Ion Monitoring Detection 2283.7.6 Results 229

3.8 Summary 230Problems 230References 232

SOLUTIONS 237

Index 263

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PREFACE

Chromatography is the most widely used technique in modern analytical chemistry. In thisbook, you will learn the fundamental principles underpinning chromatography and be ableto connect those principles to the design and use of chromatographic systems.

The focus of this book is current theory and the modern practice of chromatog-raphy. The successful practice of chromatography depends upon an understandingof molecular-level processes such as partitioning, band broadening, and the effects oftemperature and mobile phase modifiers on solute retention. In every chapter, you willfind figures and problems designed to help you visualize these processes and identify thekey variables in any given chromatography problem.

Sections such as those on microfabricated gas chromatography (GC) separations,two-dimensional liquid chromatography (2D-LC), superficially porous particles,ultra-high performance liquid chromatography (UHPLC), and Orbitrap mass spectrom-etry ensure that you are introduced to the most recent developments in chromatographyand are thus well prepared to enter the workforce.

Case studies illustrate the range of applications addressed by chromatography.Examples such as the analysis of performance-enhancing drugs in sports and the detectionof deliberate contamination of food with melamine and Sudan dyes are discussed in thecontext of liquid chromatography (LC). Chapter 3 ends with a detailed discussion of theanalysis of pharmaceutical compounds found in waterways across the United States aspart of a U.S. Geological Survey study. Chapter 2 describes a case study centered on theanalysis of Middle Eastern oil samples. This case was part of an international incident thatinvolved the United States, Iraq, Iran, and Russia, and it shows the impact of analyticalchemistry in general, and chromatography, specifically, on world affairs. All of the casestudies demonstrate how the principles and instrumentation presented earlier in thechapters contribute to solving practical, real-world problems.

This book also complements a modular approach to teaching. Rather than beingencyclopedic, this focused book allows instructors to integrate selected sections withother modular books focused on techniques such as spectroscopy or mass spectrometry,or to supplement the information provided in this book with their own materials. It alsofacilitates its use in courses such as interdisciplinary laboratory courses, biochemistry, andintroductory analytical chemistry courses.

The book has three chapters. Chapter 1 provides an in-depth description of theprocesses governing chromatography. It includes a systematic development of bandbroadening, drawing extensively from the work of J. Calvin Giddings. Numerous figures

ix

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x PREFACE

help you visualize the processes that contribute to band broadening and link thoseprocesses to key equations. Problems embedded within the chapter reinforce the connec-tions between theory, visualization, and the contributions of different factors to the overallbreadth of a peak.

Chapter 2 focuses on gas chromatography. It introduces the components of GCinstruments in the context of the function they accomplish and discusses the theorybehind instrumentation, instrument design, and practical aspects such as temperatureprogramming, injection volumes, and the selection of stationary phases and detectors thatpractitioners must consider when conducting GC analyses.

The final chapter addresses liquid chromatography. It emphasizes reversed-phaseliquid chromatography (RPLC) because of its prominence, but you will also find descrip-tions of all of the common modes of LC, including hydrophilic interaction chromatography,which has great attributes for the separation of small, polar molecules, and which mayprove to be quite valuable as a mode that is orthogonal to RPLC for two-dimensionalseparations. This chapter also discusses topics such as sub-2-μm particles, superficiallyporous particles, UHPLC, and 2D-LC as part of the mainstream modern practice of LC,preparing you with the knowledge needed to operate in modern laboratories.

There are many people to thank for the completion of this book. The sacrifices mymother made and her unflagging commitment to my education provided the foundationupon which this book exists. Each page of this book embodies her love, support, anddedication. My wife, Maura Lyons, has been a stalwart supporter throughout the process.Her love, encouragement, and even keel are irreplaceable. Thanks also to Greg Febbraro,who tracked the progress of this book through all its ups and downs. I wish we could cele-brate its publication together – your friendship is missed. Frank Settle, whose InstrumentalMethods of Analysis textbook provided the genesis for this project, has been unwaveringin his support. Some figures and text from that work have been included in this book.I owe much to Peter Carr, both for the specific work he put into reviewing material in thisbook and for the years he has spent teaching me chromatography. Leah Carr fostered anacademic family and I, like many, miss her support and affection. I am grateful to JosephBrom and Gary Mabbott for the research opportunities they provided that introduced meto instrumentation generally and to separation science specifically. The influence of theirteaching made this book possible. John Dorsey, Stephen Weber, Dwight Stoll, Charles Lucy,Paige Diamond, Teresa Golden, Brian Gregory, Brian Lamp, Yinfa Ma, David McCurdy,and James Miller all provided valuable feedback as reviewers. I appreciate the time andeffort they spent on my behalf. Much of what is right in this book is thanks to them, and allerrors are mine. Susan Boyer provided significant feedback regarding the prose. DwightStoll and Paul Boswell shared an Excel chromatogram generator that I used to createmany of the chromatograms in this book. Neal Byington at the U.S. Customs and BorderProtection was exceptionally helpful in discussions regarding the analysis of oil samplesfrom the Middle East related to the case study in Chapter 2.

MARK F. VITHA

Des Moines, IowaOctober 4, 2016

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1FUNDAMENTALS OFCHROMATOGRAPHY

Many “real-world” samples are mixtures of dozens, hundreds, or thousands of chemicals.For example, medication, gasoline, blood, cosmetics, and food products are all complexmixtures. Common analyses of such samples include quantifying the levels of drugs – bothlegal and illegal – in blood, identifying the components of gasoline as part of an arsoninvestigation, and measuring pesticide levels in food.

Chromatography is a technique that separates the individual components in a complexmixture. Fundamental intermolecular interactions such as dispersion, hydrogen bonding,and dipole–dipole forces govern the separations. Once separated, the solutes can also beidentified and quantified. Because of its ability to separate, quantify, and identify compo-nents, chromatography is one of the most important instrumental methods of analysis, bothin terms of the number of instruments worldwide and the number of analyses conductedevery day.

1.1. THEORY

Chromatography separates components in a sample by introducing a small volume of thesample at the start, or head, of a column. A mobile phase, either gas or liquid, is also intro-duced at the head of the column. When the mobile phase is a gas, the technique is referredto as gas chromatography (GC) and when it is a liquid, the technique is called liquid chro-matography (LC). Unlike the sample, which is injected as a discrete volume, the mobilephase flows continuously through the column. It serves to push the molecules in the samplethrough the column so that they emerge, or “elute” from the other end.

Two particular modes of LC and GC, known as reversed-phase liquid chromatography(RPLC) and capillary gas chromatography, account for approximately 85% of all chromato-graphic analyses performed each day. Therefore, we focus on these two techniques here andleave discussions of specific variations to the chapters that describe LC and GC in greaterdetail.

In GC, the mobile phase, which is typically He, N2, or H2 gas, is delivered from ahigh-pressure gas tank. The gas flows through the column toward the low-pressure end.The column contains a stationary phase. In capillary GC, the stationary phase is typically

Chromatography: Principles and Instrumentation, First Edition. Mark F. Vitha.© 2017 John Wiley & Sons, Inc. Published 2017 by John Wiley & Sons, Inc.

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A capillary gas chromatography column

0.5 mm

or less

10–60 m

(a)

Helium

mobile

phase

Stationary phase polymer film (0.25–5 μm)

Pore with C-18

bonded phase

Porous particles

5 μm or smaller

Liquid

mobile

phase

20–250 mm

(b)

A liquid chromatography column

4.6 mm

or smaller

Solid support

material (often

SiO2)

Particle pore

(c) (d)

1 μm 20,000X

Stationary

phase (alkyl

chains bonded

to the solid

support surface)

FIGURE 1.1 Representations of typical capillary gas (a) and liquid (b) chromatography columns. Figure(c) is a depiction of a cross section of a porous particle (shaded areas represent the solid support parti-cles, white areas are the pores, and the squiggles on the surface are bonded alkyl chains. Figure (d) isan scanning electron microscope (SEM) image of actual 3 μm liquid chromatography porous particles.Note that the lines across the particle diameters have been added to the image and are not actuallypart of particles. (Source: Alon McCormick and Peter Carr. Reproduced with permission of U of MN.).It is worth taking time to note the different dimensions involved. For the GC columns, they range frommicrons (10−6 m) for the thickness of the stationary phase, to millimeters (10−3 m) for the column diam-eter, up to tens of meters for the column length. Note also that LC columns are typically much shorterthan GC columns (centimeter versus meter).

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FUNDAMENTALS OF CHROMATOGRAPHY 3

a polymer film that is 0.25–5 μm thick (see Figure 1.1a). It is coated on the interior walls ofa fused silica capillary column with an inner diameter of approximately 0.5 mm or smaller.The column is usually 10–60 m (30–180 ft) long.

RPLC is the most common mode of liquid chromatography. In RPLC, the mobile phaseis a solvent mixture such as water with acetonitrile (CH3CN) that is forced through thecolumn using high-pressure pumps. The column is typically made of stainless steel, hasan inner diameter of 4.6 mm or smaller, and is only 20–250 mm (1–10 in.) in length (seeFigure 1.1b). However, unlike most GC columns, most LC columns are packed with tinyspherical particles approximately 5 μm in diameter or smaller, as shown in Figure 1.1c andd. When rubbed between your fingers, the particles feel like talc or other fine powders. Theparticles are not completely solid, but rather are highly porous, with thousands of pores ineach particle. The pores create cavities akin to caves within the particle. The pores create alarge amount of surface area inside the particles. A stationary phase, typically an alkyl chain18 carbon atoms long, is bonded to the surface of these pores. A more specific discussionof the important aspects of these particles, and variations in the kinds of stationary phasesbonded to them, is provided in Chapter 3. For now, it is simply important to have an imageof a stainless steel column packed with very fine porous particles that have an organic-likelayer bonded to the surface of the pores.

Some of the important RPLC and capillary GC column characteristics are summarizedin Table 1.1. We also point out here that a chromatographic analysis is conducted with aninstrument called a chromatograph and results in a chromatogram, which is a plot of the detec-tor’s response versus time (see Figure 1.2). Subsequent sections describe how retention andseparation of molecules are quantified.

1.1.1. Component Separation

Different types of molecules are separated within the column because they have differ-ent strengths of intermolecular interactions with the mobile and stationary phases. To help

TABLE 1.1 Common RPLC and GC Characteristics

RPLC GC (open tubular)

Column construction Stainless steel Quartz with a polyimidecoating

Column length 20–250 mm 10–60 mColumn inner diameter 2.1– 4.6 mm 0.1–0.5 mmParticle composition Porous silica (SiO2) particles No particles – open tubeParticle size 1.8–5 μm No particles – open tubeMobile phase Solvent mixture (e.g., water

mixed with acetonitrile)He, N2, or H2

Stationary phaselocation

Alkyl chains (C-8 and C-18)bonded to particlesurface

Liquid-like polymer filmbonded to capillary walls

Stationary phasechemistry

Relatively nonpolar andorganic in nature

Polysiloxane polymerderivatized with organicmoieties

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4 CHROMATOGRAPHY

Signal

Time0

0

FIGURE 1.2 An example of a chromatogram – a plot of signal versus time – measured using a chro-matograph (the instrument). Each peak represents a different solute that emerges from the column ata different time than the others. The peak width and height are related to the amount of each solutepresent.

(Mobile phase

analog)

(Stationary phase

analog)

Octane

Water

Toluene and phenol

introduced into the water

(mobile) phase

Toluene and phenol after

partitioning equilibrium is

achieved. Mobile phase

is enriched in phenol and

stationary phase is

enriched in toluene

CH3

CH3

OH

CH3

CH3

CH3

CH3 CH3

CH3

CH3

H3C

H3C

H3C

H3C

CH3

OH

OH

OHOH

OH

OH

OH

HO

HO HO

HO

OH

OH

CH3

CH3

CH3

CH3

H3C

H3C

H3C

CH3

CH3

CH3 CH3

CH3 CH3

OH

OH

OH

OH

OH

OH

OH

OH

OHHO

HO

OH

OH

OH

CH3

FIGURE 1.3 This figure depicts the behavior of phenol and toluene (solutes) partitioning betweenwater and octane (bulk solvents). The water and octane serve as models for the mobile and stationaryphases, respectively, in liquid chromatography. The left image depicts the system right after solutes areadded to the aqueous phase before equilibrium is established. Once equilibrium is established (right),more toluene than phenol partitions into the nonpolar octane phase. Similarly, more phenol resides inthe water due to hydrogen bonding and dipole-dipole interactions.

understand chromatographic separations, we first use a simplified model of liquid chro-matography with water as the mobile phase and octane (C8H18) as the stationary phase.Imagine that a mixture of toluene and phenol is introduced as solutes into the mobile phaseas depicted in Figure 1.3.

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FUNDAMENTALS OF CHROMATOGRAPHY 5

In this static image, given enough time, the solute molecules diffuse through the waterand into the octane. They eventually reach equilibrium, being distributed to differentextents between the water (mobile) and octane (stationary) phases. This equilibriumprocess is described in Equation 1.1

Amobile ⇌ Astationary (1.1)

with the associated equilibrium constant

K =[A]s[A]m

(1.2)

where “A” represents a specific analyte such as phenol or toluene, and K, by IUPAC def-inition, is known as the distribution constant. Many chromatographers refer to it as thepartition coefficient or distribution coefficient. We will treat all of these as synonymous inthis and the following chapters.

Because phenol is more polar than toluene and capable of hydrogen bonding withwater, it does not partition into the octane to the extent that the toluene does. Whenlooked at from a temporal perspective, phenol molecules spend less time in the octane, onaverage, than do the toluene molecules, which are attracted to the octane by dispersioninteractions. It is important to understand that phenol is also attracted to the octaneby dispersion interactions, and in fact, toluene is attracted to water through dispersionand dipole-induced dipole interactions. However, because phenol can participate indipole–dipole and hydrogen-bonding interactions with water, and toluene cannot, phe-nol has a greater affinity for the aqueous phase than does toluene. As a consequence,phenol stays in the water more and partitions less into the stationary phase than doestoluene.

It is clear from Figure 1.3 that what was once a mixture of an equal number of phe-nol and toluene molecules separates by differential partitioning between the mobile andstationary phases. It is easy to imagine that if the water phase were now drawn off andallowed to equilibrate with a fresh volume of octane, further purification of the phenolfrom the toluene would occur. Done repeatedly, eventually the phenol and toluene wouldbe completely separated from one another.

In the actual practice of chromatography, these individual, discrete steps such as justdescribed are not actually performed, but the effect of partitioning within a column is thesame. As the mobile phase is continuously introduced into the column, the solutes contin-uously partition between it and the stationary phase. Because the molecules do not movedown the column when they are in the stationary phase, those with higher affinities forthe stationary phase relative to the mobile phase, meaning those with high distributionconstants (i.e., partition coefficients), lag behind those with smaller distribution constants.In other words, some molecules elute from the column relatively quickly because theiraffinity for the mobile phase is greater than that for the stationary phase. Others, whosepartitioning favors the stationary phase, take more time to make it through the column. Forthe molecules considered in Figure 1.3, phenol elutes before toluene. In this way, differentmolecules are separated within the column based on their intermolecular interactions with

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6 CHROMATOGRAPHY

the stationary and mobile phases, which ultimately depends on the structure of the solutesand the chemical composition of the phases. The separated molecules are detected at theend of the column using a variety of detectors that can quantify, and in some cases, identifythem as they elute. The detectors used in GC and LC are described in detail in the followingchapters.

It is important to note that all molecules spend the same amount of time in the mobilephase. Therefore, the separation occurs because of different times spent in the stationary phase.To understand this, think about two canoes that start down a river at the same time, beingcarried along solely by the current. The time it takes them to go from one end of the river tothe other, without stopping, is dictated simply by the speed of the current and the length ofthe river (distance=velocity× time). If along the way, the canoes pull into a number of ports(i.e., the stationary phase), they stop their progress down the river. If one canoe stops morethan another, and stays in port for longer periods of time (i.e., has stronger interactionswith the ports), then it reaches the end of the river later than the canoe that did not stop asoften or for as long. Thus, a separation has occurred because the total time for the journeyis different for the two canoes. But still, the time spent on the river (i.e., in the mobile phase)is the same because both canoes covered the same distance and moved at the same velocitywhen on the river. Therefore, the difference in the canoes’ affinities for being in port (i.e., inthe stationary phase) caused the separation.

It should be noted that the simplified mobile and stationary phases depicted inFigure 1.3 are rough approximations to actual liquid chromatography systems, whichare discussed in more detail in Chapter 3. In addition, if the water is replaced with a gassuch as helium or nitrogen, the system approximates conditions in gas chromatography.Thus, separations in both GC and LC depend on the relative strength of intermolecularinteractions of solutes with the mobile and stationary phases. The only difference is thatin GC, because molecules do not interact with the gaseous mobile phase, the separationis dictated solely by the relative strengths of interactions of solutes with the stationaryphase.

1.1.2. Retention Factor

In the preceding section, we established that different molecules spend different amounts oftime traveling through the column. The total amount of time that a molecule spends in thecolumn, from the time of injection to the time of detection, is called the retention time, tr. Thename indicates that we think of the molecules as being retained by the column – specificallyby the stationary phase into which the solutes partition. In Figure 1.4, the retention time ofphenol is 3.3 min and toluene’s retention time is 5.2 min. While in the column, moleculesspend their time in two places – the mobile phase and the stationary phase. Thus, the totaltime they are retained is simply the sum of the time they spend in each. Hence,

tr = ts + tm (1.3)

where ts and tm are the time spent in the stationary and mobile phases, respectively.

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FUNDAMENTALS OF CHROMATOGRAPHY 7

While the retention time is the most fundamental quantity measured, we often convertit into a dimensionless quantity called the retention factor, k, where

k =tr − tm

tm(1.4)

Here, tm is a measure of the time it takes the mobile phase to flow from the start of thecolumn to the end of the column. It is often referred to as the “dead time,” or “hold-uptime.” A solute that has no affinity for the stationary phase and therefore travels down thecolumn at the same rate as the mobile phase is used to measure the dead time. This peak ismarked as tm in Figure 1.4.

Converting retention times into retention factors normalizes for some operating con-ditions that vary between columns. For example, longer columns produce longer retentiontimes even if everything else such as particle size, column diameter, and mobile phase flowrate are the same. More specifically, suppose one laboratory uses a column that is twiceas long as the one used by another laboratory. In this case, tr and tm double because themolecules have twice the distance to travel. However, Equation 1.4 shows that k is the samein both laboratories because

k =2tr − 2tm

2tm(lab with longer column)

=2(tr − tm)

2tm=

tr − tm

tm(lab with shorter column) (1.5)

Another reason for focusing on retention factors rather than retention times is that k isdirectly related to the distribution constant, which, as described above, fundamentallycontrols the separation process. To derive the relationship between the retention factor,k, and the distribution constant, K, note that Equation 1.3 can be rewritten as shown inEquation 1.6,

tr − tm = ts (1.6)

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

Signal

Time (min)

Phenol

Toluene

tm

FIGURE 1.4 Chromatogram of phenol and toluene. The retention times of phenol and toluene are3.30 and 5.20 min, respectively. The dead time, the time it takes an unretained solute to pass throughthe column, is labeled as tm.

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8 CHROMATOGRAPHY

so that Equation 1.4 can be rewritten as

k =ts

tm(1.7)

such that k reflects the ratio of the time one type of molecule (e.g., phenol) spends in thestationary phase relative to the time it spends in the mobile phase. The longer the moleculespends in the stationary phase relative to the time it spends in the mobile phase, the greaterthe value of k.

For a collection of identical molecules – for example, 100 phenol molecules – theaverage time spent in the stationary phase relative to the mobile phase also reflects theinstantaneous distribution of molecules between the phases. If molecules spend moretime, on average, in the stationary phase than in the mobile phase, then a snapshot takenat a discrete point in time shows more molecules in the stationary phase (ns) than in themobile phase (nm). Thus,

k =ts

tm=

ns

nm(1.8)

Because the molar concentration of a solute, A, is given by ni/Vi where n is the number ofmoles of A in phase i, V is the volume of phase i, and “i” is either the mobile or stationaryphase, combining Equations 1.2 and 1.8 results in

k =

[ns

Vs

]Vs[

nm

Vm

]Vm

=[A]sVs

[A]mVm= K

(Vs

Vm

)= K∕𝛽 (1.9)

where 𝛽 = Vm∕Vs and is called the “phase ratio.” It is important to note that this defini-tion of the phase ratio is the one given by the International Union of Pure and AppliedChemistry (IUPAC), but because many people define the phase ratio as 𝜙 = Vs∕Vm suchthat k = K𝜙, it is important to understand which definition is being used in different pub-lications. In this and subsequent chapters, we will follow the IUPAC definition.

The phase ratio plays a role in retention that can be understood using chemical rea-soning and logic. Going back to Figure 1.3, if more octane is added to the beaker, the ratioof octane to water increases. Furthermore, just out of sheer probability, toluene and phenolmolecules respond to the addition of octane by partitioning out of the water into the octane.Taken to the extreme, as the mobile phase volume goes to zero, all of the molecules have topartition into the stationary phase, with the consequence that ts increases and tm decreasesas shown in Figure 1.5. The result is that tr increases for all solutes. Similarly, as Vs decreasesrelative to Vm, the distribution of solutes shifts toward the mobile phase and tr decreases.

In practice, the physical characteristics of the column that one purchases dictate thephase ratio and cannot be manipulated easily. To change the phase ratio, a different col-umn must be purchased and installed in the instrument. Manipulating retention in thismanner is more frequently a consideration in gas chromatography than it is in liquid chro-matography. In GC, stationary phases with thicker polymer films bonded to the capillary

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FUNDAMENTALS OF CHROMATOGRAPHY 9

Signal

(a)

(b)

Time (min)

tm tr,A tr,B

tm tr,A tr,B

Signal

Time (min)

Larger Vm

Vs

Smaller Vm

Vs

FIGURE 1.5 Effect of decreasing the phase ratio (𝛽, Vm/Vs) by increasing Vs and decreasing Vm onretention (assuming constant Vtot). Solute retention times, tr, increase as the volume of stationary phase(Vs) in the column increases due to solutes spending more time in the stationary phase.

walls that increase retention are available. In LC, most columns have bonded phases thatare 18 carbon atoms long, although shorter chains that produce less retention are available.

EXAMPLE 1.1

We have used water and octane as models of a mobile and stationary phase in the text andwe use it again in this question. Suppose 10,000 molecules each of butylamine and methylhexanoate are added to a closed system containing 500 mL each of water and octane.The system is then shaken and allowed to come to equilibrium. The water-to-octanedistribution constant for butylamine is 0.260 and 171.8 for methyl hexanoate.1

(a) How many molecules of butylamine and methyl hexanoate are in the aqueousphase at equilibrium?

(b) Based on the calculations, which solute is more concentrated in the aqueous phaseat equilibrium?

(c) Which in the stationary phase?(d) Based on the structures of the molecules and using arguments regarding their

intermolecular interactions, rationalize the differences in the distribution con-stants for the two molecules.

(e) If more octane than water was used in the system, would the number of moles ofeach solute in the water phase increase or decrease?

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10 CHROMATOGRAPHY

Answer:

(a)

K =[butylamine]octane

[butylamine]water

=

(noctane

Voctane

)(

nwater

Vwater

) = 0.260

noctane + nwater = 10,000 so noctane = 10,000 − nwater

And we know Voctane = Vwater so the volumes cancel. Substituting yields:

K =10,000 − nwater

nwater= 0.260

10,000 = 0.260nwater + nwater = 1.26nwater

7940 = nwater for butylamine (approximately after rounding to three

significant figures)

Following the same procedure yields ∼58 molecules of methyl hexanoate inthe aqueous phase at equilibrium, meaning the other 9942 methyl hexanoatemolecules are in the octane.

(b) Butylamine is much more concentrated in the aqueous (mobile) phase, whilemethyl hexanoate is much more concentrated in the octane/stationary phase.

(c) Octane is being used to represent a stationary phase.(d) Butylamine is polar, can donate hydrogen bonds to water, can accept hydrogen

bonds from water, and has fewer carbon atoms, so it can interact well withwater. Methyl hexanoate is a larger compound with more carbon atoms, givingit stronger dispersion interactions with the octane. It is also polar (althoughless so than butylamine) and can hydrogen bond, but these effects are not asstrong and therefore water does not compete as well as the octane to attractthe methyl hexanoate.

(e) The phase ratio would shift in favor of the octane, so more molecules of bothsolutes would be found in the octane phase at equilibrium, meaning fewerthan what was calculated in part (a) would be in the aqueous phase.

Another question:The retention time of a solute is measured to be 23.76 min using gas chromatography.Under the same conditions, the dead time is 0.88 min.

(a) What is the ratio of the moles of solute in the stationary phase relative to themoles of solute in the mobile phase at any point in time during the analysis?

(b) If the column were changed to one with a larger phase ratio (i.e., larger Vm/Vs),would this ratio increase or decrease?

(c) Would the retention time increase or decrease?

Answer:

(a) k = ns

nm= 26.0 (or 26 ∶ 1) .

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FUNDAMENTALS OF CHROMATOGRAPHY 11

(b) Equation 1.9 shows that as 𝛽 increases, k decreases, so the ratio of solutesin the stationary phase relative to those in the mobile phase also decreases.An increasing phase ratio means greater volume of mobile phase relative tostationary phase. Therefore, decreasing retention makes sense because thereis less stationary phase present to retain the molecules and/or more mobilephase present for solutes to partition into.

(c) As a consequence, the retention time of the solute decreases.

1.1.3. Separation

The retention of any single component is typically not of primary importance to a chro-matographer. The idea of separation is much more important. In other words, do differenttypes of molecules elute at sufficiently different times so that they can be individually quan-tified and identified?

As Equations 1.4–1.9 show, molecules that have higher distribution constants (larger K)

1. have higher retention factors (larger k), and hence2. are retained longer, causing them to3. have higher retention times, tr,

than those with smaller distribution constants. In Figure 1.4, toluene has a higher distribu-tion constant as established in Figure 1.3 and thus elutes later than phenol. Molecules thatare retained for a long time are likely to be well separated from those that are retained fora short time.

The degree of separation between any two solutes, A and B, is quantified using aparameter called the separation factor, 𝛼.

𝛼 =kB

kA(1.10)

where “B” is the solute with the longer retention time and higher k. The “separation factor”is also frequently called “selectivity,” although IUPAC discourages this use. The words“separation factor” and “selectivity” are quite descriptive and convey the idea that the ratiomeasures the extent of separation between two solutes – in other words, how selectivelyone compound is retained relative to another on the same column.

Molecules that are well separated from one another have high separation factors,while solutes that elute close to each other have small separation factors. However,the difference in retention times is not the only factor that has to be considered whenmeasuring separation.

Consider the two chromatograms in Figure 1.6. The retention factors of both solutes arethe same in the two different chromatograms. Because the retention factors are the same, 𝛼 isthe same. Yet, the separation in Figure 1.6b is incomplete – baseline separation has not beenachieved – but in Figure 1.6a the solutes are fully resolved. Clearly, the separation factor isnot the only parameter that dictates how well resolved one component is from another.

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12 CHROMATOGRAPHY

Signal

Time

Signal

Timetm

tm(a)

(b)

FIGURE 1.6 The effect of peak width on resolution. The dead time and solute retention times are thesame in both chromatograms, meaning that the separation factor is the same in both chromatograms.The lack of resolution in (b) compared to (a) is therefore due to the widths of the peaks.

EXAMPLE 1.2

(a) Estimate the retention factors of phenol and toluene in Figure 1.4.(b) What is the separation factor of the separation?

Answer:

(a)kphenol =

tr − tm

tm= 3.30min − 0.90min

0.90min= 2.7

ktoluene =tr − tm

tm= 5.20min − 0.90min

0.90min= 4.8

.

(b) 𝛼 = 4.82.7

= 1.8.

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FUNDAMENTALS OF CHROMATOGRAPHY 13

Another question:

(a) What is the new value for the separation factor if the separation is repeatedunder conditions that lead to k=7.73 and k=9.14 for phenol and toluene,respectively?

(b) Which separation has better (i.e., higher) selectivity?

Answer:

(a) 𝛼 = 1.18.(b) The first separation has better selectivity.

1.1.4. Resolution and Theoretical Plates

Resolution between peaks is important because it makes it possible to quantify each indi-vidual component in a mixture more accurately and precisely than when peaks overlap.In the extreme case of complete overlap, quantitation is typically completely impossible(except when a mass spectrometer or an analyte-selective detector is used), and the scientistmight not even be aware that the observed peak is the result of multiple components.

Figure 1.6b makes it clear that in addition to the separation factor, the width of the peaksis important in terms of resolution. Thus, a consideration of the processes contributing topeak widths follows.

In order to fully understand the physical processes that occur within a chromato-graphic column that lead to peak broadening, also known as “band broadening,” it is firstimportant to be able to quantify peak widths. Ideally, chromatographic peaks elute witha Gaussian profile, as shown in Figure 1.7. Two measures of peak widths are commonly

0

50

100

150

200

250

300

350

400

7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4

Sig

nal

Time (min)

(a)

Wb

FIGURE 1.7 (Continued)

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14 CHROMATOGRAPHY

0

50

100

150

200

250

300

350

400

7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4

Sig

na

l

Time (min)

W1/2

Maximum peak signal

½ of the maximum signal

(b)

FIGURE 1.7 Illustration of the two different measurements of width: (a) baseline width (Wb) and (b) fullwidth at half maximum (FWHM, W1/2).

used, the baseline peak width (Wb) and the peak width at half maximum height (W1∕2). The

baseline peak width is found by drawing tangents to the curve as shown in Figure 1.7aand determining the distance between the two tangents at the baseline of the peak. To findW1∕2

the highest signal reached by the peak is found (300 in Figure 1.7b) and divided in half(note however, that while the maximum signal is 300, the baseline is at 20, so the actualsignal height is 280); hence, the “half maximum” refers to half the maximum signal. Thewidth of the peak, in time units, is then found at the corresponding 1∕2-height as shown(i.e., at 140+ 20, or 160). Naturally, broader peaks have greater values of W1∕2

and Wb thando narrower peaks, as depicted in Figure 1.8.

7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5

Sig

na

l

Time

W1/2

Wb

FIGURE 1.8 Illustration showing that narrower peaks have smaller Wb and W1/2 than do broaderpeaks.

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FUNDAMENTALS OF CHROMATOGRAPHY 15

EXAMPLE 1.3

(a) Estimate W1/2 and Wb for the peak shown (hint: note that the signal baseline isalready at 20).

9.059.008.958.908.850

20

40

60

80

Sig

na

l

100

120

140

Time (min)

9.10 9.15

Answer:W1/2 =0.093 min, Wb =0.16 min.

The half-width should be measured at a signal of 70 because the total height is120, but the baseline is at 20. So the actual peak height is 100 signal units tall. Halfof this is 50, added to the baseline of 20, indicates that the half-width occurs ata signal strength of 70. The answers given here were obtained by blowing up animage of the peak and estimating the results using a ruler, so values differ slightlydepending on the methodology used. The important points are (1) understandingthe two measures and how they differ and (2) that the width at half-height is notsimply half of the baseline width.

(b) This question is aimed at showing why peak width is important. Imagine a chro-matogram with the following four peaks:

Peak tr (min) W1/2

1 3.00 0.102 4.00 0.103 6.00 0.504 7.00 0.50

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16 CHROMATOGRAPHY

Notice that peaks 1 and 2 are separated from each other by 1.00 min, as are peaks3 and 4. Accurately sketch the chromatogram. Which peaks are better separated(i.e., not overlapping), peaks 1 and 2 or peaks 3 and 4? What do you concludeabout peak widths and their influence on separation?

Answer:Peaks 1 and 2 are better separated because they have narrower peak widths. Whileboth sets of peaks are separated by the same time difference, wider peaks canoverlap, making the peaks poorly resolved and therefore difficult to quantify. Thisis why we measure peak widths in practice and devote a lot of discussion in thesections below to factors that affect peak widths.

To make comparisons between different columns, the concept of “theoretical platenumber,” symbolized by N, was introduced. The concept of “plates” is borrowed fromdistillation columns that have actual plates in the interior (see Figure 1.9). A mixture isheated to boiling at the bottom and a temperature gradient develops along the verticalaxis of the column, with cooler temperature at the top. The vapor created by the boilingliquid is enriched in the more volatile components. As this vapor mixture rises, it cools andcondensese on the plates. Hot vapors rising up through the column reheat the condensedliquid, causing it to vaporize again, further enriching the vapor in the more volatilecomponents. This process of volatilization and condensation occurs continuously. Theresult is that the more volatile components are increasingly enriched near the top of thecolumn, leaving the higher-boiling species enriched near the bottom. In industrial distil-lation processes, the vapor exiting the top of the column, now significantly enriched orcomposed entirely of the most volatile component, can be condensed. As the temperatureof the remaining mixture continues to increase, the less volatile components also exitthe column and can be collected. Collecting different fractions at different points in timeresults in separation or at least partial purification of the components. Columns with moreplates, and thus plates that are closer together, produce better separations that result in purercomponents being isolated from the original mixture. It should be noted that the fractionaldistillation columns that are used in chemical laboratories use glass beads, glass protru-sions, or other packing material to provide the surface on which the vapors condenseas they rise. In this case, the column does not have plates per se, but its performance isstill described by the concept of “theoretical plates,” as discussed in the following in thecontext of chromatography.

Chromatography columns do not have discrete, individual plates either and do notseparate components based on a temperature gradient along the length of the column, butthe theory of plates was borrowed as a way to quantify a chromatographic column’s abilityto separate the chemicals in a mixture and to compare columns to each other.

The number of theoretical plates for a chromatographic column is given by

N =(

tr

𝜎

)2

= 5.54

(tr

W1∕2

)2

(1.11)

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FUNDAMENTALS OF CHROMATOGRAPHY 17

AA

AA

AA

A

AA

A A

B

B

BB B

B BBB B

B

BC

C CC C

CC C

C

CC

C

C

DD

DDD

D

DD

D

DE

EE

E

E

E

EE E

EEE

E

F

FF F

B

C C

E

F

B

C

D D

E

FFFFF

DF

FD

CCE EFAB

C DF

B DE F

C

D

A

AA

AA

AAA

A BAB

B BB B

BBB

B

C CC C

CC

C

CC C

C DD

DDD DD

DDEE

EE

EEE E

EEEF

FF F

B

C C

B

C

D D

E

F E

FFFFF

B DEEA CD

FF

BDC C

C

D

CE EFAB

C DF

B DE F

A A

Collection cups or "plates"

Plate

height Plate

height

Pure A

Pure B

Pure C

Pure D

Pure E

Pure F

Mixture of

A and B

Mixture of

C and D

Mixture of

E and FMixture of

C, D, and E

Mixture of

compounds

A, B, C, D, E,

and FHot

Cool

Liquid condensing and

draining into collecting

plates as vapor rises

and cools

Heat Heat

FIGURE 1.9 A mixture of compounds A, B, C, D, E, and F separated with two different distillationcolumns. The compound volatility follows the order: volatility of A> volatility of B> · · ·> volatility of F.The column on the left has more plates and smaller plate heights (the distance between plates). Thisleads to a more complete separation of the components of the mixture compared to that achievedwith the column on the left with fewer plates and larger plate heights. Chromatography columns donot have actual, physical plates inside them like the distillation columns pictured here, but the con-cept is borrowed as a way to measure and compare the separation ability of different columns. Thecolumns depicted here have around 10–20 actual plates, whereas GC and LC columns have thousandsor hundreds of thousands of “theoretical plates.”

where 𝜎 is the standard deviation of the solute peak. The second equality in Equation 1.11is used because W1∕2

is easier to measure quickly from a chromatogram than is the standarddeviation of the peak. The factor 5.54 assumes that the peak is Gaussian in shape.

Equation 1.11 is essentially a measure of how broad a solute band gets for a given timeit spends in the column (hence, tr/W1∕2

). Columns in which solutes can reside for a longtime (large tr) but still produce narrow peaks (small W1∕2

) have high N values. Columns